Can any triangle be inscribed in any convex figure? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T22:42:06Z http://mathoverflow.net/feeds/question/35710 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/35710/can-any-triangle-be-inscribed-in-any-convex-figure Can any triangle be inscribed in any convex figure? Dan Brumleve 2010-08-16T02:21:37Z 2010-08-16T05:15:07Z <p>Can any triangle be inscribed in any convex figure? i.e. given a convex figure and a triangle can we transpose and scale and rotate that triangle so that its vertices are on the boundary of the convex figure?</p> http://mathoverflow.net/questions/35710/can-any-triangle-be-inscribed-in-any-convex-figure/35715#35715 Answer by Victor Protsak for Can any triangle be inscribed in any convex figure? Victor Protsak 2010-08-16T03:32:48Z 2010-08-16T03:32:48Z <p>A more general result is known: if \$C\$ is any Jordan curve and \$T\$ is a triangle then there exists a triangle similar to \$T\$ inscribed in \$C.\$ Moreover, the vertices of such triangles are dense in \$C.\$ See the references in the Wikipedia article on the <a href="http://en.wikipedia.org/wiki/Inscribed_square_problem#Variants_and_generalizations" rel="nofollow">Inscribed Square Problem</a>.</p>